The present invention relates to a wireless transmission system, and in particular, relates to such a system which improves the privacy characteristics by scrambling the spectrum of input signals, and keeps transmission power constant irrespective of spectrum scrambling. In particular, the present invention relates to a mobile communication system which transmits a signal through a PM (phase modulation) system.
FIG. 1(a) shows a conventional PM transmission system, in which the numeral 1 is an input terminal, 2 is a PM modulator, 3 is a transmission antenna, and the symbol (a) shows an observation point. FIG. 1(b) is the modification of FIG. 1(a), and has a spectrum scrambler which performs the privacy function. In FIG. 1(b), the numeral 4 is an input terminal, 5 is a spectrum scrambler, 6 is a PM modulator, and 7 is a transmission antenna, and the symbols (b) and (c) are observation points.
The transmission modulation index Dev.sub.PM of FIG. 1(a), and the modulation index Dev.sub.EX of FIG. 1(b) are given in the meaning of effective power as shown as follows. ##EQU1## where Dev.sub.PM is the transmission modulation index in FIG. 1(a), Dev.sub.EX is the transmission modulation index in FIG. 1(b), G(f) is power spectrum of arbitrary input signals, S(*) is spectrum scramble function, f is frequency, and f.sub.1 and f.sub.2 are lower and upper limits of the pass band (which is 0.3 to 3 kHz domain in a mobile telephone system).
Input signals of telephone communication are usually speech signals. FIG. 2 shows the power spectrums of speech signals, and the long time average G(f) is approximated to G(f)=G.sub.0 f.sup.-2, where G.sub.0 is a constant, and the frequency band [f.sub.1, f.sub.2 ] in a mobile wireless telephone communication is [0.3, 3] kHz.
Now, the analysis of the modulation index Dev.sub.PM when a spectrum scrambling is introduced is carried out below, under the strict condition of the spectrum scrambling with a simple spectrum inversion. The symbol S'[*] shows a spectrum inversion, and is shown below. EQU S'[G(f)]=G(f.sub.0 -f), f.sub.0 =f+f.sub.2, f.epsilon.[f.sub.1, f.sub.2 ](3)
The modulation index Dev.sub.PM and Dev.sub.EX are deduced by substituting the equation (3) into eqs (1) and (2), respectively.
When a signal G(f) is applied to the point (a), the modulation index Dev.sub.PM is given below. ##EQU2## When the signal G(f) is applied to the point (b), the signal T.sub.EX having the following power spectrum is obtained at the point (c). EQU T.sub.EX (f)=S'[G(f)]=G(f.sub.0 -f)
Accordingly, the modulation index Dev.sub.EX in case of spectrum inversion is given by equation (5). ##EQU3##
Comparing the equation (4) with the equation (5), the insertion of a spectrum inversion unit before the PM modulator as shown in FIG. 1(b) increases the modulation index by 10 log (Dev.sub.EX /Dev.sub.PM)=8.7 dB (power ratio), and it causes consequently the disadvantage of increasing the frequency bandwidth.
FIG. 3 is another prior art method for preventing said increase of the frequency bandwidth. In FIG. 3, the numeral 8 is an input terminal, 9 is a PM modulator, 10 is a transmission antenna, 11 is an attenuator, 12 is a spectrum invertor, 13 is a PM modulator, and 14 is a transmission antenna. The PM modulator 9 and the antenna 10 provide a transmitter for speech signals without any spectrum inversion, and the combination of th attenuator 11, the spectrum invertor, the PM modulator 13 and the antenna 14 provides a transmitter for speech signals with spectrum inversion. However, the use of an attenuator has the disadvantage that a signal to noise ratio (S/N) is deteriorated.
FIG. 4 is still another prior art method for overcoming the increase of the frequency bandwidth, and is shown in the article "Voice quality improvement using compandor and/or emphasis on frequency spectrum inverted secrecy system" in 161 J64-B, No. 5, Pages 425-432, May 1982 published by the Institute of Electronics and Communication in Japan. In FIG. 4, the numeral 15 is an input terminal, 16 is a spectrum inverter, 17 is a pre-emphasis circuit, 18 is a PM modulator, and 19 is an antenna. The symbols (d) and (e) are observation points.
The equipment of FIG. 4 functions to provide the same modulation index Dev.sub.EX with secrecy as the modulation index Dev.sub.PM without secrecy, only when a spectrum scrambler is a simple spectrum inverter, and an input signal if G(t). This is shown below.
When input signals G(t) are applied to the input terminal 15, simple spectrum inverted signals G(f.sub.0 -f) appear at the point (d), and these signals are emphasized by the pre-emphasis circuit 17 (H.sub.p (f)), and the signals T.sub.EX (f) appear at the point (e). EQU T.sub.EX (f)=H.sub.p (f)G(f.sub.0 -f) (6)
where: ##EQU4## Subsequently, Dev.sub.EX is shown as follows. ##EQU5## Eq. 9 shows clearly that Dev.sub.EX coincides with Dev.sub.PM. However, when speech signals are arbitrary (G(t)), that coincidence between Dev.sub.EX and Dev.sub.PM is not satisfied even when a spectrum scrambler is restricted to be a simple spectrum inverter. The analysis for a general speech signal is shown below. ##EQU6## Accordingly; ##EQU7## When a new variable x is introduced to be f.sub.0 -f, df=-dx, the equation (11) becomes to; ##EQU8## The equation (12) is converted to the equation (13) by changing -dx to dx. ##EQU9## On the other hand, the modulation index Dev.sub.PM for non-inverted speech signal is expressed as follows. ##EQU10## Comparing the equation (13) with the equation (14), it is apparent that Dev.sub.EX does not coincide with Dev.sub.PM in case of general input signal G(t) being employed.
The equipment of FIG. 4 solves merely the problem in a very limited case, that is, input signals are restricted to be G(t), and a spectrum scrambler is a simple spectrum inverter, then, Dev.sub.EX =Dev.sub.PM is satisfied. However, the circuit of FIG. 4 has still the disadvantages that the modulation index and/or the frequency spectrum is increased by introducing a spectrum scrambling process, if input speech signals are general, or if a spectrum scramble is not a simple spectrum inversion.
A general spectrum scramble divides input signals spectrum to plural sub-frequency bands within the input frequency domain, and the scramble changes the location of each of the divided sub-frequency bands. Accordingly, if an emphasis is introduced, that emphasis must be designed for each combination of sub-frequency bands, and of course that is almost impossible without any increase in circuit implementation. Therefore, it has been impossible to provide a constant modulation index irrespective of general spectrum scrambling.